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system of equations is shown below.

y = -3x – 4

-9x – 3y = -2

Which statement about the ordered pair (1, -7) is true?
Responses
A It is not a solution to either equation.It is not a solution to either equation.
B It is the only solution to the system. It is the only solution to the system.
C It is one of many solutions to the system.It is one of many solutions to the system.
D It is a solution to the first but not the second equation.

1 answer

To determine which statement about the ordered pair (1, -7) is true, we need to test whether this pair is a solution to each of the given equations.

  1. Testing the first equation:

    The first equation is: \[ y = -3x - 4 \]

    Substituting \(x = 1\) and \(y = -7\): \[ -7 = -3(1) - 4 \] \[ -7 = -3 - 4 \] \[ -7 = -7 \] This is true, so (1, -7) is a solution to the first equation.

  2. Testing the second equation:

    The second equation is: \[ -9x - 3y = -2 \]

    Substituting \(x = 1\) and \(y = -7\): \[ -9(1) - 3(-7) = -2 \] \[ -9 + 21 = -2 \] \[ 12 \neq -2 \] This is false, so (1, -7) is not a solution to the second equation.

Now we can summarize our findings:

  • (1, -7) is a solution to the first equation.
  • (1, -7) is not a solution to the second equation.

Thus, the correct response is:

D: It is a solution to the first but not the second equation.